A duality principle for homogeneous vector fields with applications

[en] We introduce a duality principle for homogeneous vectorfields. As an application of this duality principle, stability and boundedness results for negative order homogeneous differential equations are obtained, starting form known results for positive order homogeneous differential equations.

Disciplines :

Electrical & electronics engineering

Author, co-author :

Moreau, Luc

Aeyels, Dirk

Peuteman, Joan

Sepulchre, Rodolphe ; Université de Liège - ULiège > Dép. d'électric., électron. et informat. (Inst.Montefiore) > Systèmes et modélisation

Language :

English

Title :

A duality principle for homogeneous vector fields with applications

Publication date :

2002

Journal title :

Systems and Control Letters

ISSN :

0167-6911

eISSN :

1872-7956

Publisher :

Elsevier Science, Amsterdam, Netherlands

Volume :

Issue :

Pages :

37-46

Peer reviewed :

Peer Reviewed verified by ORBi

Available on ORBi :

since 29 November 2010

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Bibliography

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Peuteman J., Aeyels D. (1999) Averaging results and the study of uniform asymptotic stability of homogeneous differential equations that are not fast time-varying. SIAM J. Control Optim. 37(4):997-1010.
Peuteman J., Aeyels D., Sepulchre R. (2000) Boundedness properties for time-varying nonlinear systems. SIAM J. Control Optim. 39(5):1408-1422.
Rosier L. Etude de quelques problèmes de stabilisation, Ph.D. Thesis, Paris XI, Chapitre III: General symmetries for ordinary differential equations, Application to stability and controllability; 1993.
Yoshizawa T. Stability Theory by Liapunov's Second Method, The Mathematical Society of Japan, Tokyo, Japan; 1966.

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